Journal of the Mathematical Society of Japan

Boundedness of fractional integral operators on Morrey spaces and Sobolev embeddings for generalized Riesz potentials

Yoshihiro MIZUTA, Eiichi NAKAI, Takao OHNO, and Tetsu SHIMOMURA

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Our aim in this paper is to deal with boundedness of fractional integral operators on Morrey spaces L(1,φ)(G) and the Sobolev embeddings for generalized Riesz potentials. Target spaces are Orlicz-Morrey, Orlicz-Campanato, and generalized Hölder spaces.

Article information

J. Math. Soc. Japan, Volume 62, Number 3 (2010), 707-744.

First available in Project Euclid: 30 July 2010

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Zentralblatt MATH identifier

Primary: 26A33: Fractional derivatives and integrals
Secondary: 31B15: Potentials and capacities, extremal length 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems

Sobolev embeddings Morrey space Orlicz space Riesz potential fractional integral


MIZUTA, Yoshihiro; NAKAI, Eiichi; OHNO, Takao; SHIMOMURA, Tetsu. Boundedness of fractional integral operators on Morrey spaces and Sobolev embeddings for generalized Riesz potentials. J. Math. Soc. Japan 62 (2010), no. 3, 707--744. doi:10.2969/jmsj/06230707.

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